投资风险收益、多目标规划（约束法、线性加权）

姚安欣/mm1.m

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+%投资利益与风险1998A题
+
+
+%模型一 给定风险承受程度，求最大利益
+f=[-0.05,-0.27,-0.19,-0.185,-0.185];
+
+%A矩阵
+%A=[0,0.025,0.015,0.055,0.026];         %错误
+%b=[1,1,1,1,1];
+A=[zeros(4,1),diag([0.025,0.015,0.055,0.026])];%不等式约束条件矩阵
+
+%Aeq、beq
+Aeq=[1,1.01,1.02,1.045,1.065];
+beq=1;
+
+%lb
+%lb=0;                  %错误
+lb=zeros(5,1);
+
+
+%可承担风险率a
+a=(0:0.001:0.05);
+
+%保存最优解
+Q=zeros(1,length(a));
+xx=[];%空矩阵存放最优解对应x的值
+for i=1:length(a)
+    b=a(i)*ones(4,1);
+    [x,y]=linprog(f,A,b,Aeq,beq,lb);
+    Q(i)=-y;%注意取负！！！
+    xx=[xx;x'];
+end
+plot(a,Q,'*r');
+xlabel("风险率");
+ylabel("最大收益");
+
+
+%模型二 收益、风险按权重组合
+% f0=[-0.05,-0.27,-0.19,-0.185,-0.185];
+% w=(0:0.1:1);
+% Aeq=[1,1.01,1.02,1.045,1.065,0];
+% beq=1;
+% lb=0;
+% xx=[];
+% Q=zeros(1,length(w));
+% A=[zeros(5,1),diag([0.025,0.025,0.055,0.065,0])];
+% b=ones(5,1);
+% for i=1:length(w)
+%     f=[-w(i)*f0,1-w(i)];
+%     b=x(end)*b;
+%     [x,y]=linprog(f,A,b,Aeq,beq,lb);
+%     Q(i)=-y;
+%     xx=[xx,x'];
+% end
+% plot(w,Q,'*r');
+
+%模型二 收益、风险按权重组合
+clc; clear; close all; format long g;
+
+M = 10000;
+prob = optimproblem;
+x = optimvar('x', 6, 1, 'LowerBound', 0);
+r = [0.05, 0.28, 0.21, 0.23, 0.25];
+p = [0, 0.01, 0.02, 0.045, 0.065];
+q = [0, 0.025, 0.015, 0.055, 0.026]';
+%w = 0:0.1:1;
+w = 0.7:0.03:1;
+V = [];
+Q = [];
+X = [];
+
+prob.Constraints.con1 = (1 + p) * x(1:end-1) == M;
+prob.Constraints.con2 = (q(2:end).* x(2:end-1))<= x(end);        %下标从1开始
+
+for i = 1:length(w)
+    prob.Objective = w(i) * x(end) - (1 - w(i)) * (r - p) * x(1:end-1);     %注意大小写
+    [sol, fval, flag, out] = solve(prob);
+    xx = sol.x;
+    V = [V, max(q.* xx(1:end-1))];
+    Q = [Q, (r - p) * xx(1:end-1)];
+    X = [X, xx];
+    
+    plot(V, Q, '*-');
+    grid on;
+    xlabel('风险');
+    ylabel('收益');
+end
+
+
+
+%模型三：达到一定盈利水平，极小化风险
+
+clc; clear; close all; format long g;
+M=10000;
+k=1500:100:3000;
+prob = optimproblem;
+x = optimvar('x', 5, 1, 'LowerBound', 0);%下界为0
+r = [0.05, 0.28, 0.21, 0.23, 0.25];
+p = [0, 0.01, 0.02, 0.045, 0.065];
+q = [0, 0.025, 0.015, 0.055, 0.026]';
+
+V = [];
+Q = [];
+X = [];
+t = optimvar('t', 'LowerBound', 0);
+
+%prob.Objective=max(q.*x);%极小化风险
+for i=1:length(k)
+    prob.Objective = t; % 极小化风险
+    prob.Constraints.con1 = (1 + p) * x == M;
+    prob.Constraints.con2=((r-p)*x>=k(i));%达到一定盈利水平
+    prob.Constraints.con3=(q.*x<=t);
+    [sol,fval,flag,out]=solve(prob);
+    if flag==1
+        xx=sol.x;
+        X=[X,xx];
+        Q=[Q,(r-p)*xx];
+        V=[V,fval];
+    else
+        xx=-1*ones(5,1);
+        X=[X,xx];
+        Q=[Q,-1];
+        V=[V,-1];
+    end
+
+
+end
+plot(k,V,'*-');
+
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